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Directed Polymers in Restricted Geometries

Published online by Cambridge University Press:  15 February 2011

G. Zumofens ,
J. Klafter  and
A. Blumen
G. Zumofens
Affiliation:
Physical Chemistry Laboratory, ETH-Zentrum, CH-8092 Zürich, Switzerland
J. Klafter
Affiliation:
School of Chemistry, Tel-Aviv University, Tel-Aviv, 69978 Israel
A. Blumen
Affiliation:
Theoretical Polymer Physics, University of Freiburg, W-7800 Freiburg, Germany
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Abstract

We study numerically directed polymers in random potential fields for one-dimensional and fractal substrates. For fractal substrates the time evolution of the mean transverse fluctuations depends besides on the randomness of the potential also on the fractal nature of the substrate. The two effects enter in a subordinated way, i.e. the corresponding characteristic exponents due to the potential and the substrate combine multiplicatively. For a one-dimensional substrate the propagator P(x, t), the probability distribution of the transverse displacement x(t), follows the scaling form P(x, t) ∼ 〈x2(t)〉-1/2f (ξ), where ξ is the scaling variable ξ = x/〈x2(t)〉1/2. The numerical results support the scaling function f (ξ) ∼ exp (-cξδ) with δ > 2 which indicates an “enhanced” Gaussian behavior. These results are compared with those of a related “toy model”.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 290: Symposium N – Dynamics in Small Confining Systems , 1992 , 19
Copyright
Copyright © Materials Research Society 1993

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